Dynamics of Reversible Networks

We present a model for dynamics of entangled networks made up of linear chains with many temporary cross-links. At times shorter than the lifetime of a cross-link such networks behave as elastic rubbers (gels). On longer time scales the successive breaking of only a few cross-links allows the chain to diffuse along its confining tube. The motion of a chain in this hindered reptation model is controlled by the concentration and lifetime of tie points. We calculate the self-diffusion coefficient and discuss the stress relaxation in terms of molecular parameters, including the chain length, the number of cross-linking groups per chain, and the lifetime and probability of formation of cross-links. We find good agreement with recent experiments by Stadler et al. on model thermoplastic elastomers.